Three Dimensional Geometry

Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the point R(1,3,3) is 5, then the square of the area of PQR is equal to :

1. 148
2. 144
3. 136
4. 140

Answer

(3) 136

Solution

Point on the line through P: Q=(-2+3t, -1+2t, 3+2t), t 0

[figure]

QR2=25 17t2-34t=0 t=2 Q=(4,3,7)

PR=|(3,4,0)|=5=QR isosceles; PQ= 68, height h= 25-17= 8

(Area)2= ( 12 68 8 )2=136

Answer: (3)